Chapter 3: Coordinate Geometry

Understanding Coordinates

What are Coordinates?

Every point on the plane has an "address" - its coordinates!

Written as: (x,y)(x, y) where:

  • xx = horizontal distance from origin (abscissa)
  • yy = vertical distance from origin (ordinate)

Key Vocabulary

TermMeaningExample
Abscissax-coordinateIn (3,5)(3, 5), abscissa = 3
Ordinatey-coordinateIn (3,5)(3, 5), ordinate = 5
Ordered pair(x,y)(x, y) together(3,5)(3, 5) is an ordered pair

ORDER MATTERS!

(3,4)≠(4,3)(3, 4) \neq (4, 3)

  • (3,4)(3, 4): Go right 3, then up 4
  • (4,3)(4, 3): Go right 4, then up 3

These are completely different points!

Reading Coordinates from a Graph

Steps:

  1. From the point, draw a perpendicular to x-axis
  2. Where it hits x-axis = x-coordinate
  3. From the point, draw a perpendicular to y-axis
  4. Where it hits y-axis = y-coordinate

Points on the Axes

LocationCoordinatesExample
On x-axis(a,0)(a, 0)(5,0)(5, 0), (−3,0)(-3, 0)
On y-axis(0,b)(0, b)(0,4)(0, 4), (0,−2)(0, -2)
Origin(0,0)(0, 0)The center!
Visualizer
Coordinate Plane
XYOP(5, 0)Q(0, 4)O(0, 0)Q I (+,+)Q II (-,+)Q III (-,-)Q IV (+,-)
Point P: (5, 0)
Quadrant IV

Interactive Visualization